While Shakespeare wrote the play Romeo and Juliet in Elizabethan times, the play actually refers to history that took place in Medieval times. Therefore, the education Romeo and Juliet would have received would have been the education noble class children received in the Medieval ages.
For the most part, noble children were taught at home with tutors. The noble classes were expected to fight in the kings' wars as knights; therefore, a boy's education primarily focused on preparing him for the knighthood. Training for the knighthood began at about the age of six or seven. Boys were taught hunting, horsemanship, how to wear armor, and how to handle swords and lances. Hence, the fact that Romeo was a skilled swordsman shows that he had already received his training in the knighthood ("Aristocratic Education in Europe"). Some Medieval boys might have been educated in grammar schools. Education was limited to the wealthy, though the higher up in social rank the boys were, the more likely they were to be taught by private tutors ("Aristocratic Education in Europe"). Whether they were taught in grammar schools or by private tutors, a boy's education would have also focused on Latin, religious studies, as well as grammar, rhetoric, logic, philosophy, mathematics, and astronomy ("Medieval Education").
It was not typical for girls in the Medieval ages to receive a formal education. Only girls in the noble class, like Juliet, would have been educated. Like the boys, they would have also been taught at home by private tutors. However, since girls, as women, would be expected to care for the home and provide entertainment, their education focused on housekeeping, sewing, weaving, spinning, and embroidery ("Aristocratic Education in Europe"). Also, like the boys, girls were taught to ride horses, but not to fight. Girls would have also been taught to read, write, speak foreign languages like French and Latin, and also how to dance, play music, and sing.